Just reporting back that, contrary to the advice received above, I did in fact get the business class hotel (assuming Skylight is still the business class hotel)

Not sure if it's policy for *A status or if I just lucked out, but the pre-printed voucher was waiting for me at check-in for my first flight. Either way, this works out well, because my plan for the layover was to attend a cultural dinner and get a few drinks at a bar, and Skylight seems to offer good options for both